Method and device for calculating dialysis efficiency

ABSTRACT

Methods and apparatus for calculating a parameter of mass exchange of a solute fluid are disclosed including passing the solute in a predetermined volume of the fluid on one side of a semi-permeable membrane in a dialyzer, passing an exchange fluid on the other side of the semi-permeable membrane, obtaining a concentration curve by repeatedly measuring the concentration of a solute such as urea in the mass exchange fluid, fitting an approximate curve having a logarithm comprising a substantially straight line with at least a portion of a concentration curve, determining a parameter of the approximation curve, and calculating the mass of urea in the predetermined volume of fluid by the formula m=(Q d ×c d )/P where P is the mass of the urea, Q d  is the flow rate of the exchange fluid, C d  is the concentration of the urea in the exchange fluid, and P is the parameter.

FIELD OF THE INVENTION

The present invention relates to a method and apparatus for calculatingdialysis efficiency using values obtained from a urea sensor for thecalculations. The calculations can also predict certain conditions whichmay require intervention.

BACKGROUND OF THE INVENTION

In hemodialysis it is common to dialyse a patient three times per week,with time periods of three to four hours per treatment. The object ofthis treatment is to provide an adequate dose of dialysis to thepatient. Such a dose of treatment can be defined in different ways.

One commonly used definition uses the urea molecule as a marker moleculeand prescribes that the dialysis clearance (K) divided by thedistribution volume (V) of urea times total treatment time (t) shouldexceed a certain constant, for example Kt/V is greater than one pertreatment. The weekly dialysis dose is then Kt/V greater than three.

One common way of measuring Kt/V is by measuring the concentration ofurea (c_(b)) in the plasma before and after the treatment. The ratioR=c_(bpost)/c_(bpre) is correlated to Kt/V. A number of differentequations have been suggested for the calculation of Kt/V, such as:

Kt/V=−ln (R−0.03)+(4−3.5·R)·UF/W  (1)

where UF=ultrafiltration volume removed in liters and W=post-dialysisweight in kg.

Several clinical studies have been performed evaluating Kt/V in whichpost-dialysis plasma urea (c_(bpost)) has been measured immediatelyafter the dialysis, usually less than two minutes after ending thetreatment. However, most patients have a rebound of c_(bpost). If anequilibrated post-treatment (c_(bpost)) is measured after about 30minutes, for example, a more “true” Kt/V can be measured.

The measurement of c_(b) is not unproblematic. It is required that ablood sample be taken before and after the dialysis treatment. Suchsamples are then analysed by the hospital's laboratory. The resultingvalues are thus provided with a substantial time delay. In this way itis not possible to adjust the actual treatment so that a prescribed doseis obtained.

The post-treatment sample must be taken with care, especially regardingtiming, to avoid false values due to cardiopulmonary or accessrecirculation. Another source of error is the rebound mentioned above.

If an equilibrated post-treatment sample should be taken, such sampleshould be taken about 30 to 60 minutes after terminating the treatment,which is not practical for the patient. The amount of rebound and therate of rebound varies considerably from patient to patient.

These problems have been addressed in the prior art in differentmanners.

International Application No. WO 94/08641 describes the use of a ureamonitor for assessing the adequacy of an dialysis treatment. The ureamonitor is connected to the dialysis effluent line and measures theconcentration of urea in the dialysate leaving the dialyzer.

According to this specification, it is necessary to know or measure thepre-dialysis plasma urea value (c_(bpre)). Such measurements can be madeby measuring the urea concentration in an equilibrated sample takenbefore initiation of the treatment. However, such initial measurementtakes time and the dialysis machine needs to be specially constructed toobtain such pre-dialysis urea value.

Other indicators of adequate dialysis are URR and SRI:

URR=1−R=1−c _(b post) /c _(b pre)  (2)

SRI=(m _(urea pre) −m _(urea post))/m _(urea pre)  (3)

where m_(urea pre) and m_(urea post) are pre and post amounts of urea inthe body, respectively.

The object of the present invention is to provide a method and apparatusfor determining the efficiency of a dialysis treatment and monitoringdelivered dose of treatment on-line.

Another object of the present invention is to provide a method andapparatus for continuously monitoring the dialysis efficiency foradjusting the dialysis treatment on line when required, for example ifthe dialyzer is clotted.

A further object of the present invention is to provide a method andapparatus for estimating the dose of dialysis delivered without the needfor taking blood samples or requiring the dialysis machine to make anyspecial adjustments such as taking an equilibrated pre-dialysis plasmaurea concentration.

SUMMARY OF THE INVENTION

In accordance with the present invention, these and other objects havenow been realized by the invention of method for calculating a parameterof the mass exchange of a solute in a fluid comprising:

passing the solute in a predetermined volume of the fluid on one side ofa semi-permeable membrane in a mass exchange device,

passing an exchange fluid on the other side of the semi-permeablemembrane,

obtaining a solute concentration curve by repeatedly measuring theconcentration of the solute in the exchange fluid,

fitting an approximation curve having a logarithm comprising asubstantially straight line with at least a portion of the concentrationcurve,

determining a parameter of the approximation curve, and

calculating the mass of the solute in the predetermined volume of thefluid by the formula m=Q_(d)·c_(d)/P wherein

m comprises the mass of the solute,

Q_(d) comprises the flow rate of the exchange of fluid,

c_(d) comprises the concentration of the solute in the exchange fluid,and

P comprises the parameter.

In a preferred embodiment, the method includes determining the flow rateof the exchange fluid, integrating the product of the flow rate of theexchange fluid and the concentration of the solute in the exchange fluidover time in order to calculate the accumulated mass of the solute inthe exchange fluid, and calculating a solute reduction index by theformula:

SRI=(U−G·t)/(m+U−G·t)

 wherein

SRI comprises the solute reduction index,

U comprises the accumulated mass of the solute in the exchange fluid,

G comprises the production of the solute over time, and

t comprises time.

In accordance with one embodiment of the method of the presentinvention, the mass exchange device comprises a dialyzer, the massexchange fluid comprises a dialysate fluid, and the solute comprisesurea.

In accordance with another embodiment of the method of the presentinvention, the parameter corresponds to a whole body clearance dividedby the predetermined volume of the fluid.

In accordance with another embodiment of the method of the presentinvention, the passing of the exchange fluid on the other side of thesemi-permeable membrane comprises passing a finite initial concentrationof the solute and wherein the measuring of the solute concentrationcomprises repeatedly measuring the difference of the soluteconcentration across the semi-permeable membrane.

In accordance with another embodiment of the method of the presentinvention, the fitting of the approximating curve comprises obtaining acompensated concentration by subtracting a predetermined concentrationterm from the concentration of the solute, obtaining the logarithm ofthe compensated concentration, and fitting a straight line to thelogarithm of the compensated concentration, whereby the predeterminedconcentration term compensates for the generation of the solute.

In accordance with another embodiment of the method of the presentinvention, the parameter of the approximation curve comprises a slope ofthe substantially straight line.

In accordance with another embodiment of the method of the presentinvention, the fitting of the approximation curve excludes apredetermined initiation period. Preferably, the predeterminedinitiation period comprises about 60 minutes.

In accordance with another embodiment of the method of the presentinvention, the method includes periodically interrupting the passing ofthe exchange fluid on the other side of the semi-permeable membrane fora first time period, and adjusting the time scale by replacing the firsttime period with a second time period, the second time period being lessthan the first time period.

In accordance with another embodiment of the method of the presentinvention, the parameter comprises a slope with respect to time in thefollowing equation:

ln (c _(d) −G/Q _(d))=ln (c ₀ −G/Q _(d))−Kt/V  (I)

wherein

c_(d) comprises the concentration of the solute in the exchange fluid,

G comprises the production of the solute over time,

c₀ comprises the concentration of the solute in the exchange fluid attime zero,

K/V comprises the relative whole body dialysis efficiency, and

t comprises the time from time zero.

In a preferred embodiment, the method includes determining the momentarymass by the equation:

m ₁=(Q _(d) ·c _(d1))/(K/V)₁

wherein

(K/V)₁ is determined in accordance with equation (I), and includingdetermining the momentary relative efficiency at a predetermined time bythe equation:

(K/V)₂=(Q _(d) ·c _(d2))/m ₂

wherein

(K/V)₂ comprises the momentary relative efficiency,

m₂ comprises m₁−(U₂−U₁)+G (t₂−t₁),

c_(d1) comprises the concentration of the solute in the exchange fluidat time t₁,

c_(d2) comprises the concentration of solute in the exchange fluid attime t₂,

U₁ comprises the accumulated mass of the solute in the exchange fluid attime t₁, and

U₂ comprises the accumulated mass of the solute in the fluid at time t₂.In a preferred embodiment, the method includes integrating the relativedialysis efficiency over time, whereby an estimate of the total dialysisdosage can be obtained.

In accordance with another embodiment of the method of the presentinvention, the fitting of the approximation curve comprises calculatinga line passing through the greatest number of points in the logarithm ofthe concentration curve. Preferably, the calculating is compensated.

In accordance with another embodiment of the method of the presentinvention, the method includes calculating the momentary mass from allvalues of the concentration of the solute in the exchange fluid from thesubstantially straight line within a predetermined time period,calculating a calculated initial mass from the momentary mass, andestimating the actual initial mass from the calculated initial mass.Preferably, estimating of the actual mass comprises determining the meanor median value of the calculated initial mass.

In accordance with another embodiment of the method of the presentinvention, the method includes determining the momentary mass of thesolute in the exchange fluid by determining the actual concentration ofthe solute in the exchange fluid by a method selected from the groupconsisting of analyzing a blood sample and equilibrating the exchangefluid with blood and determining the distribution value of the solute.

In accordance with another embodiment of the method of the presentinvention, the method includes estimating the distribution volume of thefluid, and determining the concentration of the solute in the fluid bydividing the calculated mass by the distribution volume. Preferably,estimating of the distribution volume is carried out utilizing Watson'sformula.

In accordance with another embodiment of the method of the presentinvention, the method includes measuring the concentration of the solutein the fluid and determining the distribution volume of the solute inthe fluid by dividing the calculated mass and the concentration of thesolute in the fluid.

In accordance with another embodiment of the method of the presentinvention, the method includes introducing a disturbance into thedialyzer and measuring the resulting effect in the dialysate, wherebythe concentration of the solute in the fluid is measured, calculatingthe effective clearance of the dialyzer from the measured resultingeffect on the dialysate, calculating the plasma water concentration ofthe solute utilizing the formula

c _(pw) =Q _(d) ·c _(d) /K _(e)

wherein

c_(pw) comprises the plasma water concentration of urea upon initiationof the dialysis,

Q_(d) comprises the effluent dialysate flow rate from the dialyzer,

c_(d) comprises the concentration of urea extrapolated to initiation ofthe dialysis, and

K_(e) comprises the effective clearance of the dialyzer for urea; and

determining the distribution volume of the urea in the fluid by means ofthe formula:

V=m ₀ /c _(pw)

 wherein

m₀ comprises the initial mass.

In accordance with another embodiment of the method of the presentinvention, the method includes determining a deviation of theconcentration curve from the approximation curve, and emitting an alarmbased upon the deviation with respect to a predetermined thresholdlevel.

In accordance with another embodiment of the method of the presentinvention, the parameter comprises the slope of ln(c_(d)−c_(k)) as afunction of (V₀/UF)ln(V/V₀) in the equation:

ln (c _(d) −c _(k))=ln (c ₀ −c _(k))+[(K−UF)/V ₀]·[(V ₀ /UF) ln (V/V₀)]  (II)

wherein

c_(d) comprises the concentration of the dialysate at time t,

c₀ comprises the concentration of the dialysate at time zero,

c_(k) comprises G/[Q_(d) (1−UF/K)],

G comprises the generation of the solute,

Q_(d) comprises the flow rate of the dialysate,

K comprises the whole body clearance,

V₀ comprises the distribution volume prior to treatment,

UF comprises the ultrafiltration per unit time, and

[(K−UF)/V₀] comprises the slope.

Preferably, the method includes determining the momentary mass accordingto the equation:

m ₁=(Q _(d) ·c _(d1))/(K/V)₁

wherein

(K/V)₁=(K/V₀)/(1−t₁·UF/V₀)

and (K/V₀) is determined according to equation (V) and includingestimating UF/V₀, wherein the momentary relative efficiency at a giventime is determined according to the equation:

(K/V)₂=(Q _(d) ·c _(d2))/m ₂

 wherein

m ₂ =m ₁−(U ₂ −U ₁)+G (t ₂ −t ₁)

 and

c_(d1) comprises the concentration of the dialysate at time t₁,

c_(d2) comprises the concentration of the dialysate at time t₂,

U₁ comprises the accumulated mass of the solute at time t₁, and

U₂ comprises accumulated mass of the solute at time t₂.

In accordance with the present invention, apparatus has also beenprovided for calculating a parameter of a mass exchange procedurecomprising:

mass exchange means for passing a solute in a predetermined volume of afluid on one side of a semi-permeable membrane and passing a massexchange fluid on the other side of the semi-permeable membrane in orderto exchange the mass of the solute therebetween;

measuring means for measuring the concentration of the solute in themass exchange fluid, whereby a solute concentration curve can beprovided;

first calculation means for fitting an approximation curve having alogarithm comprising a substantially straight line to at least a portionof the solute concentration curve;

second calculation means for determining a parameter of theapproximation curve; and

third calculation means for calculating the mass of the solute in thepredetermined volume of the fluid by means of the formula

m=(Q _(d) ·c _(d))/P

 wherein

m comprises the mass of solute in the predetermined volume of the fluid,

c_(d) comprises the concentration of the solute in the mass exchangefluid,

P comprises the parameter, and

Q_(d) comprises the flow rate of the mass exchange fluid.

In accordance with another embodiment of the apparatus of the presentinvention, the apparatus includes flow rate determination means fordetermining the flow rate of the mass exchange fluid,

fourth calculation means for calculating the accumulated mass of thesolute in the mass exchange fluid from the mass exchange flow rate andthe concentration of the solute by integrating the product of the massexchange flow rate and the solute concentration in the mass exchangefluid over time, and

fifth calculation means for calculating a solute reduction indexaccording to the formula:

SRI=(U−G·t)/(m+U−G·t)

 wherein

SRI comprises the solute reduction index,

G comprises the production of the solute over time, and

t comprises time.

In accordance with another embodiment of the apparatus of the presentinvention, the mass exchange means comprises a dialyzer, the exchangingof the solute between the sides of the semi-permeable membrane comprisesdialysis, the mass exchange fluid comprises a dialysate fluid, and thesolute comprises urea. In accordance with a preferred embodiment, theapparatus includes flow rate measuring means for measuring the flow rateof the dialysate, and wherein the third calculation means includes meansfor calculating the accumulated mass of the urea in the dialysate byintegrating the product of the flow rate of the dialysate and theconcentration of the solute in the dialysate fluid over time.

In accordance with another embodiment of the apparatus of the presentinvention, the dialysate fluid has an initial concentration of the ureawhich is greater than zero, and wherein the measuring means measures theconcentration difference across the semi-permeable membrane.

In accordance with another embodiment of the apparatus of the presentinvention, the first calculation means includes means for subtracting afirst compensation term comprising G/Q_(d) from the concentration of theurea in order to obtain a compensated concentration, whereby a straightline can be fitted to the logarithm of the compensated concentration sothat the compensation term compensates for the production of the ureaover time.

In accordance with another embodiment of the apparatus of the presentinvention, the parameter comprises the slope of the substantiallystraight line.

In accordance with another embodiment of the apparatus of the presentinvention, the first calculation means includes means for excluding dataobtained during the initiation period. Preferably, the initiation periodcomprises about 60 minutes.

In accordance with another embodiment of the apparatus of the presentinvention, the first calculation means includes means for adjusting thetime scale whereby when the flow of the dialysate fluid is interruptedfor a first time period the first time period can be replaced with asecond time period, the second time period being shorter than the firsttime period.

In accordance with another embodiment of the apparatus of the presentinvention, the parameter comprises the slope with respect to time, andwherein the second calculation means includes means for calculating theparameter by means of the following equation:

ln (c _(d) −G/Q _(d))=ln (c ₀ −G/Q _(d))−Kt/V  (I)

wherein

c_(d) comprises the concentration of the dialysate at time t,

G comprises the generation of the urea,

Q_(d) comprises the flow of the dialysate fluid,

c₀ comprises the concentration of the dialysate fluid at time zero,

K/V comprises the relative dialysis efficiency, and

t comprises the time from time zero.

In accordance with another embodiment of the apparatus of the presentinvention, the second calculation means includes means for calculating amomentary mass according to the equation:

m ₁=(Q _(d) ·c _(d1))/(K/V)₁

wherein

m₁ comprises the momentary mass, (K/V)₁ is determined according toequation (I), and the momentary relative efficiency at any time isdetermined according to the equation:

(K/V)₂=(Q _(d) ·c _(d2))/m ₂

 wherein

(K/V)₂ comprises the momentary relative efficiency,

m ₂ =m ₁−(U ₂ −U ₁)+G (t ₂ −t ₁),

c_(d1) comprises the concentration of the dialysate fluid at time t₁,

c_(d2) comprises the concentration of the dialysate fluid at time t₂,

U₁ comprises the accumulated mass of the dialysate fluid at time t₁, and

U₂ comprises the accumulated mass of dialysate fluid at time t₂.

Preferably, the second calculation means comprises means for integratingthe relative dialysis efficiency over time whereby an estimate of thetotal dialysis dose is provided.

In accordance with another embodiment of the apparatus of the presentinvention, the second calculation means comprises means for fitting theapproximation curve by calculating a line passing through the greatestnumber of points in the logarithm of the concentration curve.Preferably, the calculation means includes means for calculating themomentary mass of the solute using the values of the concentration ofthe solute in the mass exchange fluid within a predetermined limit fromthe substantially straight line which can then be used to calculate theinitial mass of the solute, which can be used to estimate the actualinitial mass of the solute.

In accordance with another embodiment of the apparatus of the presentinvention, the second calculation means further includes means forestimating the actual initial mass based upon the median or mean valueof the initial mass.

In accordance with another embodiment of the apparatus of the presentinvention, the apparatus includes means for determining a momentary massof the solute by analyzing a blood sample or by equilibration of thedialysate with blood and determining the actual concentration of thesolute and measuring the distribution volume of the solute.

In accordance with another embodiment of the apparatus of the presentinvention, the apparatus includes means for estimating the distributionvolume of the dialysate and for determining the concentration of theurea in the dialysate by dividing the calculated mass by the volume.Preferably, the means for estimating the distribution volume utilizesWatson's formula.

In accordance with another embodiment of the apparatus of the presentinvention, the apparatus includes means for measuring the concentrationof the urea in the dialysate and for determining the distribution volumeby dividing the calculated mass by the concentration.

In accordance with another embodiment of the apparatus of the presentinvention, the measuring means comprises means for introducing adisturbance into the dialyzer, means for measuring the resulting effectin the dialysate and for calculating the effective clearance of thedialyzer from the resulting measurements, means for calculating theplasma water concentration of the solute by the formula:

c _(pw) =Q _(d) ·c _(d) /K _(e)

wherein

c_(pw) comprises the plasma water concentration of urea at theinitiation of the dialysis,

Q_(d) comprises the flow rate of the dialysate,

c_(d) comprises the concentration of the urea extrapolated to theinitiation of the dialysis procedure,

K_(e) comprises the effective clearance of the dialyzer for urea,

and including means for determining the distribution volume V of theurea using the formula V=m₀/c_(pw) where V comprises the distributionvolume.

In accordance with another embodiment of the apparatus of the presentinvention, the apparatus includes means for determining a deviation ofthe concentration curve from the approximation curve and alarm means foremitting an alarm upon deviation greater than a predetermined thresholdlevel.

In accordance with another embodiment of the apparatus of the presentinvention, the parameter comprises a slope and wherein the secondcalculation means comprises means for calculating the slope in theequation:

ln (c _(d) −c _(k))=ln (c ₀ −c _(k))+[(K−UF)/V ₀][(V₀ /UF) ln (V/V₀)]  (II)

wherein

[(K−UF)/V₀] comprises the slope of a predetermined line,

ln(c_(d)−c_(k)) comprises the line,

c_(d) comprises the concentration of the dialysate at time t,

c_(k) comprises G/[Q_(d) (1−UF/K)],

G comprises the generation of the urea,

Q_(d) comprises the flow of the dialysate,

c₀ comprises a concentration of the dialysate at time zero,

K/V comprises the relative dialysis efficiency, and

UF comprises the ultrafiltration over time.

In accordance with another embodiment of the apparatus of the presentinvention, the second calculation means includes means for calculating amomentary mass according to the equation:

m ₁=(Q _(d) ·c _(d1))/(K/V)₁

wherein

(K/V)₁=(K/V ₀)/(1−t ₁ ·UF/V ₀),

(K/V₀) is determined according to equation (V) and UF/V₀ is estimated,and the momentary relative efficiency at any given predetermined time isdetermined according to the equation:

(K/V)₂=(Q _(d) ·c _(d2))/m ₂

 where

(K/V)₂ comprises the momentary relative efficiency,

m ₂ =m ₁−(U ₂ −U ₁)+G (t ₂ −t ₁)

 and

c_(d1) comprises the concentration of the urea at time t₁,

c_(d2) comprises the concentration of the urea at time t₂,

U₁ comprises the accumulated mass of the urea at time t₁ and

U₂ comprises the accumulated mass of the urea at time t₂.

According to the present invention, a urea monitor is used for measuringthe urea concentration c_(d) in the effluent dialysate from a dialyzerand for determining the total removed urea (U) during the treatment. Themeasured values are used by a computer for estimating a pre-dialysisurea mass m₀ and the relative efficiency, K/V. Using these values, anindication of the dose of dialysis can be obtained on-line, for exampleby integrating the calculated value K/V over the treatment time. Sincethe pre-dialysis and post-dialysis urea masses are calculated, SRI canbe determined. URR can be determined as well if the distribution volumeis estimated, for example with Watson's formula, see equations (2) and(3) above. Also, equation (1) could be used since R is known. It isnoted that SRI and URR are obtained as equilibrated values.

According to another approach of the present invention, it is assumedthat the relative efficiency K/V is comparatively stable over at leastsmaller time periods and decreases continuously. If a sudden change inefficiency is determined, it could be an indication of an errorcondition possibly requiring nurse intervention, such as clotting of thedialyzer, or a change of blood flow Q_(b).

According to still another approach of the present invention, theeffective clearance of the dialyzer is determined by introducing adisturbance into the dialyzer and analyzing the effluent dialysate fromthe dialyzer in view of the disturbance. The disturbance can be analteration of the conductivity of the dialysis fluid. By analysis of theresults, it is possible to determine the effective clearance of thedialyzer. By combining the dialysate concentration of urea and theeffective clearance of the dialyzer, the blood concentration of urea canbe determined without the need for any invasion. By combination with theamount of urea obtained by the present invention, the distributionvolume of urea can be estimated.

The measured concentration values of urea in the effluent dialysatesolution has a scattered appearance, for many reasons. However, by usinga special curve adaptation algorithm, it is possible to evaluate therelative efficiency, K/V, over periods where it is relatively constantin order to accurately determine relevant dialysis parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention may be more fully appreciated with reference tothe following detailed description, which, in turn, refers to thedrawings in which:

FIG. 1 is a schematic view of a dialysis machine intended for use inhemodialysis including a urea monitor in which the invention can beused;

FIG. 2 is a schematic view similar to FIG. 1, but with the urea monitorintegrated in the dialysis machine;

FIG. 3 is a schematic view similar to FIG. 1 of a dialysis machineadapted for use in hemofiltration;

FIG. 4 is a schematic view similar to FIG. 2 of a dialysis machineadapted for use in hemofiltration;

FIG. 5 is a diagram of concentration values over time obtained from theurea monitor in the dialysis machine according to any one of FIGS. 1-4;

FIG. 6 is a diagram of an estimate of initial urea mass in the diagramaccording to FIG. 5;

FIG. 7 is a diagram similar to FIG. 5, but showing a dialysis treatmenthaving a problematic portion;

FIG. 8 is a diagram of an estimate of the initial urea mass in thediagram according to FIG. 7;

FIG. 9 is a schematic view similar to FIG. 2, including means forinducing a disturbance in the dialyzer; and

FIG. 10 is a diagram similar to FIG. 5 for determining the bloodconcentration of urea.

DETAILED DESCRIPTION

The present invention is intended to be used to estimate parameters fora dialysis treatment, such as hemodialysis, hemodiafiltration orhemofiltration. It can also be used for some types of peritonealdialysis. However, the present invention is not limited to theabove-mentioned treatment modes, but can also be used for non-medicalpurposes.

FIG. 1 is a schematic diagram of a dialysis machine with which thepresent invention can be practised. The dialysis machine provides meansfor replacing the renal function of a mammal if the renal function isimpaired or completely absent.

The blood from a patient is removed into an extracorporeal circuit 2including a filter or dialyzer 1, including a semi-permeable membrane 3.The blood passes on one side of the membrane. On the other side of themembrane, a dialysis fluid is circulated by the dialysis machine 4.

The dialysis fluid is usually prepared by the machine from one or moreconcentrates and water to form a dialysis fluid having the desiredproperties. Thus, the machine disclosed in FIG. 1 comprises a waterinlet 5, two concentrate inlets 6 and 7, and two concentrate meteringpumps, 8 and 9. A first main pump 10 propels the prepared dialysis fluidto the dialysis side of the dialyzer into contact with the membrane.

A second main pump 11 passes the effluent fluid from the dialyzer, theinlet dialysis fluid and any ultrafiltrate removed from the bloodthrough the filter, further on to an outlet 12 and to the drain.

A by-pass line 13 is arranged between the first pump 10 and the secondpump 11. Several valves, 14, 15, and 16, are arranged for controllingthe flow of dialysis fluid. The valves and the pumps are controlled by acomputer 17 as schematically shown by several lines in FIG. 1. Ofcourse, the dialysis machine is provided with several other means, as isconventional. These other means are not disclosed, since they are notrelevant for the operation of the present invention.

The first main pump 10 is driven at a speed such that the dialysis fluiddelivered to the dialyzer is substantially constant, e.g., about 500ml/min. The second main pump 11 is driven with a slightly higher speedso that the effluent fluid, called the dialysate, has a flow rate ofe.g., about 515 ml/min. This operation generates a pressure at thedialysate side of the dialyzer, which is suitable for removing about 15ml/min of ultrafiltrate fluid from the blood, i.e. plasma water. Duringa treatment period of 4 hours, such ultrafiltration means a fluidremoval from the patient of about 3.6 liters. Of course, the dialysismachine is operated so that the treatment prescribed for the patient isfulfilled.

In the effluent line from the dialysis machine there is a urea monitor18, which measures the urea concentration c_(d) in the effluentdialysate. The monitor can be positioned either inside the dialysismachine or completely outside the dialysis machine. The urea monitor canbe of the type disclosed in International Application No. WO 96/04401.It is noted that this urea monitor has a conductivity sensor, so theconductivity of the dialysate is determined by the urea monitor and theurea concentration is calculated using such conductivity measurements.

The urea monitor is shown connected to the computer 17 of the dialysismachine. However, the monitor can have a computer of its own.

The urea sensor or the dialysis machine also includes means formeasuring the flow rate of the effluent dialysate, Q_(d). The computer17 is arranged to provide concentration values c_(d) as well as valuesof the total mass of urea, U, removed during the treatment as theintegral of Q_(d)·c_(d). The concentration values are taken continuouslyso that a concentration curve, c_(d), can be obtained from the ureasensor as well as a mass curve, U.

FIG. 2 discloses a similar dialysis machine to that of FIG. 1. The maindifference is that in this case the urea monitor 19 is placed betweenthe dialyzer 1 and the second main pump 11 and before the outlet of thebypass line.

FIG. 3 discloses a similar dialysis machine to that of FIG. 1, but inthis case adapted for hemofiltration or hemodiafiltration. The onlydifference is that in this case there is included an infusion line 20including an infusion pump 21. The infusion line 20 starts from theoutlet of the first main pump 10 and ends at the blood inlet side of thedialyzer, for providing an infusion fluid to the blood upstream of thedialyzer, called preinfusion. The urea monitor 22 is arranged in theeffluent dialysate line downstream of the second pump 11.

Finally, FIG. 4 discloses a similar dialysis machine to that of FIG. 2,but in this case adapted for hemofiltration or hemodiafiltration andproviding an infusion fluid to the blood downstream of the dialyzer,called postinfusion. The urea monitor 23 is placed before the secondmain pump 11 and before the outlet of the bypass line.

FIG. 5 discloses a typical urea concentration curve, c_(d), obtainedfrom the urea sensor. As appears from this figure, the curve is veryirregular and includes several dips. These dips are obtained when thedialysis machine is connected for self-calibration, when valve 16 isopened and valves 14 and 15 are closed.

FIG. 6 is a plot of urea mass values calculated according to the methoddisclosed in further details below.

FIG. 7 is a concentration curve obtained during a treatment having someproblematic portions, as also described further below.

Finally, FIG. 8 is a plot of urea mass values calculated according tothe method disclosed below.

There are several approaches to urea kinetics. One common approach isbased on the assumption that urea is distributed in a single bodycompartment, namely the single pool model. It is well known that themeasured urea concentration during treatments does not follow such amodel, specially at high efficiency treatments.

Another approach assumes that the urea is distributed in two distinctseries connected body pools with a diffusive exchange of ureatherebetween. This model can explain the noted rebound after treatment,and the more rapid removal of urea at the beginning of the treatment.

Still another approach assumes that the body is divided into severalcompartments communicating with the blood with different time delays.

In the present invention, a urea monitor is used to measure ureaconcentration in the effluent dialysate from a dialyzer. Moreover, thetotal amount of effluent dialysate is measured. Thus, it is possible todetermine the urea concentration, c_(d), times the total dialysate flow,Q_(d). By integrating the product of c_(d)·Q_(d), the total removedurea, U, is obtained.

If it is assumed that there is no accumulation of urea in the body, thetotal amount of removed urea (U) must be equal to urea generated (G) inthe body over a certain time period, for example averaged over one week.This can be used for calculating the nutrition status or proteincatabolic rate (PCR).

According to the present invention, the urea concentration measured by aurea monitor in the effluent dialysate solution from the dialyzer, isused for determining parameters of the dialysis as it progresses. Theseparameters are used for assessing the dialysis treatment on-line todetermine the efficiency, the delivered dose, pre and post total ureamasses in the body, the urea generation rate, the volume of distributionof urea in the body (for example by taking a blood sample fordetermining the urea concentration in the blood), and still furtherparameters and variables as will become evident in the description tofollow.

These estimations according to the present invention are independent ofany assumptions about the distribution of urea in the body.

Thus, the present invention starts from the fact that no assumptionshould be made about the urea distribution in the body. Instead, thetotal amount of urea (m) in the body at each moment is considered.According to the present invention, the definition of mean ureaconcentration is the mean concentration of urea in the body over adistribution volume (V).

Neither the distribution volume, nor the mean urea concentration can bemeasured, but we can use them for calculations. They can, however, bemeasured indirectly through the urea concentration measured in theeffluent dialysate by the urea monitor as explained below.

Moreover, according to the present invention, the normally used dialyzerclearance is replaced by a whole body clearance K defined as the ratiobetween urea mass removal rate and mean urea concentration, c_(m), inthe body. The urea mass removal rate is measured by the urea monitor andis the urea concentration (c_(d)) in the effluent dialysate times theeffluent dialysate flow (Q_(d)). Consequently, these definitions are:

K=Q _(d) ·c _(d) /c _(m)  (4)

m=c _(m) ·V  (5)

Since the rate of change of the urea mass in the body is the ureageneration rate (G) minus the urea mass removal rate, Q_(d)·c_(d), thefollowing equation is valid:

dm/dt=G−Q _(d) ·c _(d) =G−m·K/V  (6)

This is a first order differential equation with time-varyingcoefficients which can be solved by standard methods. If we presume thatK and G are constant and that V is a linear function of t (V=V₀−UF·t),we find that: $\begin{matrix}\begin{matrix}{{\int_{0}^{T}{\frac{K}{V}\quad {s}}} = {\ln \lbrack \frac{m_{0} - \frac{G \cdot V_{0}}{K - {UF}}}{m_{T} - \frac{G \cdot V_{T}}{K - {UF}}} \rbrack}} \\{= {- {\ln \lbrack {1 - \frac{m_{0} - {m_{T}{G \cdot T \cdot \frac{UF}{K - {UF}}}}}{m_{0} - \frac{G \cdot V_{0}}{K - {UF}}}} \rbrack}}} \\{= {- {\ln \lbrack {1 - \frac{U - {G \cdot T \cdot \frac{{KT}/V_{0}}{{{KT}/V_{0}} - {\Delta \quad {W/V_{0}}}}}}{m_{0} - \frac{G \cdot T}{{{KT}/V_{0}} - {\Delta \quad {W/V_{0}}}}}} \rbrack}}}\end{matrix} & (7)\end{matrix}$

The assumption made for arriving at equation (7) is that the whole bodyclearance K is constant throughout the treatment.

Alternatively, it can be assumed that the relative efficiency K/V isconstant, which results in a similar equation: $\begin{matrix}{{\int_{0}^{T}{\frac{K}{V}\quad {s}}} = {\ln \lbrack \frac{m_{0} - \frac{G \cdot V_{0}}{K}}{m_{T} - \frac{G \cdot V_{T}}{K}} \rbrack}} & (8)\end{matrix}$

However, we have found that K and K/V, respectively, are not constantthroughout the complete treatment, but are usually larger during aninitial period of the treatment during the first 30 to 60 minutes, andare then approximately constant.

Moreover, equations (7) and (8) require the initial amount of urea, m₀,which must be measured prior to the dialysis treatment, for example by ablood sample or by equilibrated dialysate as described in InternationalApplication No. WO 94/08641, and by estimating the distribution volumeof urea in the body.

However, the need for taking an equilibrated blood sample about 30 to 60minutes after the treatment has been eliminated since the equationcalculates the accumulated Kt/V continuously so that the treatment canbe terminated when the desired dose has been achieved.

Another object of the present invention is to take a further step inusing the data obtained from the urea monitor to obtain all data neededfor estimating important parameters of the complete treatment. By usingthe idea of whole body urea mass and whole body clearance, K, it ispossible to develop equations which are independent of any assumptionabout constant clearance, K, or constant relative efficiency, K/V, overthe complete treatment period.

By combining equations (4) and (5), and by integrating the left portionof equation (6) we obtain:

m=(Q _(d) ·c _(d))/(K/V)  (9)

and

m=m _(o) +G·t−U  (10)

where

G=urea generation which is assumed constant

U=total removed urea, which is equal to the integral of Q_(d)·c_(d)obtained from the urea monitor.

By rearranging we obtain:

K/V=(Q _(d) ·c _(d))/(m _(o) +G·t−U)  (11)

or

m _(o) +G·t=U+(Q _(d) ·c _(d))/(K/V)  (12)

Equations (11) and (12) are independent of any assumptions of the ureadistribution in the body or any assumption of constant K. The onlyassumption made is that G is constant. However, if G is not constant,the product G·t should be replaced by the integral of G over t.

Equation (11) can be used to evaluate the time dependence of K/V, whichcan be used for some purpose to be explained in more details below.

Like the case with equations (7) and (8), it is necessary to obtain theinitial amount of urea m₀ in the distribution volume V of the body forequations (11) and (12).

It is possible to obtain that value by taking a blood sample beforeinitiation of the dialysis and by estimating the distribution volume,for example by using Watson's formula.

Another method is to allow the dialysate to equilibrate with the bloodat initiation of the dialysis treatment and measure the dialysateconcentration, whereby the dialysate concentration equals the bloodwater concentration. By estimating the distribution volume, for exampleby Watson's formula, the initial mass of urea, m₀, can be obtained.

By these methods, it is possible to obtain a value of the initial mass,m₀, of urea, which can be used in equation (11) for obtaining themomentary relative efficiency, K/V. By integrating K/V over time, anestimate of the delivered dose, Kt/V, is obtained.

On the average, Watson's formula gives a good estimate of thedistribution volume for a population of patients. However, the error fora specific patient may be large and difficult to predict. This mayresult in a large error in the estimate of initial mass, m₀.

On the other hand, and according to the present invention, it has nowbeen found that the initial mass, m₀, can be calculated by using onlythe data obtained from a urea monitor, which measures the ureaconcentration, c_(d), in the effluent dialysate from a dialyzer and theflow of dialysate, Q_(d).

We can see that the left portion of equation (12) is a straight linewith the slope G. The variables c_(d) and Q_(d) as well as U(dU/dt=Q_(d)·c_(d)) are measured by the urea monitor. If we know K/V inat least two points, it is possible to calculate the constants m₀ and G.

It is also possible to determine G from the total removed urea duringone week, which should be equal to the generation if steady state ispresumed, i.e. the generation equals the removal. If the patient isdialysed three times per week, the removed urea during one such dialysistreatment can be used for estimating the generation, as disclosed byGarred et al.

If the constant m₀ is calculated from several measured values, it ispossible to obtain a more accurate value of m₀ by taking the mean valueor median value or other statistical value from all calculated values ofthe constant m₀.

In order to continue further, it is necessary to make an assumptionabout the time dependence of K/V.

Firstly, it is assumed that the instantaneous relative efficiency K/V isconstant over at least some time period during the treatment. Thedialysis curves obtained seem to validate the fact that there should beat least some periods with constant K/V, at least in dialysis with lowultrafiltration UF. It can be assumed that V is a linear function oftime with constant ultrafiltration. However, it seems that the clearanceK also varies with time in a similar manner, at least over certain timeperiods.

Taking the derivative of equation (12) with constant K/V we obtain:

G=dU/dt+Q _(d)·(V/K)·dc _(d) /dt  (13)

By inserting dU/dt=Q_(d)·c_(d) we obtain: $\begin{matrix}{{\frac{c_{d}}{t} + {\frac{K}{V}c_{d}}} = {\frac{G}{Q_{d}} \cdot \frac{K}{V}}} & (14)\end{matrix}$

By integrating and taking the logarithm of equation (14) we obtain:

ln (c _(d) −G/Q _(d))=ln (c ₀ −G/Q _(d))−Kt/V  (15)

The curve of equation (15) is a straight line with the slope K/V. Asappears from equation (15), the dialysate concentration value, c_(d),has to be reduced by an offset term G/Q_(d) related to the generation.

Thus, by using equation (15) in a period where the slope of the curve isconstant, the momentary relative efficiency K/V can be determined in anumber of points. Thus, by using equation (12), m₀ can be calculated foreach point and an averaged (mean or median) value of m₀ can beestimated.

Secondly, it is assumed that K is constant over at least some timeperiod during the treatment. The dialysis curves obtained seem tovalidate the fact that there should be at least some periods withconstant K. We also presume that during said time period thedistribution volume of urea in the body V is a linear function of time twith a constant ultrafiltration UF:

V=V ₀ −UF·t  (16)

By taking the derivative of equation (12) we obtain:

 G=dU/dt+(Q _(d) ·V/K)dc _(d) /dt−(Qd·c _(d) /K)·dV/dt  (17)

which results in:

dc _(d) /dt+c _(d)·(K−UF)/V=(K/V)·G/Q _(d)  (18)

Equation (18) can be solved as follows: $\begin{matrix}{{{c_{d}(t)} - \frac{G}{Q_{d}( {1 - {{UF}/K}} )}} = {\{ {{c_{d}(0)} - \frac{G}{Q_{d}( {1 - {{UF}/K}} )}} \} \cdot ( \frac{V}{V_{0}} )^{\frac{K - {UF}}{UF}}}} & (19)\end{matrix}$

The expression G/[Q_(d) (1−UF/K)]=c_(k) is an offset term for themeasured dialysate concentration, c_(d), due to urea generation G. Thedialysis concentration, c_(d), will approach this offset c_(k)asymptotically for long treatment times.

Thus:

ln (c _(d) −c _(k))=ln (c ₀ −c _(k))+[(K−UF)/V ₀]·[(V ₀ /UF) ln (V/V₀)]  (20)

where

[(V ₀ /UF) ln (V/V ₀)]=(V ₀ /UF) ln (1−t UF/V ₀)≡−t  (21)

By plotting the left-hand side of equation (20) versus [(V₀/UF)ln(V/V₀)]it is possible to determine the slope [(K−UF)/V₀]. The ultrafiltrationUF is constant and known. Thus, the relative efficiency K/V₀ can bedetermined, if UF/V₀ is estimated. By using equation (12), m₀ can bedetermined, if the urea generation (G) is known. Otherwise, the ureageneration can be determined as the time varying component of thedetermined m₀.

The determination of m₀ is made only over the time period where it isfound that K or K/V, respectively, are constant, i.e. where the measureddata fit equations (15) or (20) well enough.

As can be seen from the enclosed diagram, FIG. 3, over a dialysateconcentration curve from a typical patient, c_(d) is very irregular dueto, inter alia, bypass periods, cell-to-cell checks in the urea monitor,noise and changes in the treatment efficiency (K/V) for various reasons.

It is not easy to find a curve which is the best fit for a certain timeperiod where K or K/V should be constant. However, the Hough transform(see, U.S. Pat. No. 3,069,654), used for finding lines in images, is amethod capable of handling such types of disturbances. The Houghtransform looks for straight lines that passes through the largestnumber of points. Therefore, even if a large number of points areoutside the line, this method can still work. It will also find severallines, if there are changes in the treatment efficiency.

According to the preferred embodiment of the present invention, thefollowing steps are performed.

The urea generation rate, G, is estimated from patient data, for examplefrom the amount of urea removed during a week.

A continuous measurement is performed in the effluent dialysate of ureaconcentration, c_(d). At the same time, the urea concentration, c_(d),times the dialysate flow rate, Q_(d), is integrated to provide the totalremoved urea, U.

The measurement is started at time zero, which is defined as the timewhere the measurement of urea concentration exceeds a certain levelduring more than five minutes.

From time zero, the urea concentration, c_(d), is plotted versus time,and the total removed urea, U, is calculated by integrating the ureaconcentration, c_(d), times Q_(d).

Then, there is a waiting period of, for example, about 60 minutes, whereit is assumed that K or K/V may be changing.

After the waiting period, the data of the urea concentration curve isprocessed by subtracting the offset term G/Q_(d) from the ureaconcentration, c_(d), and plotting the logarithm of the corrected ureaconcentration. Then, the curve is processed for finding a portion whereK/V is substantially constant, as discussed above in connection withequation (15). This is performed by using the Hough transform of findinga line which passes through the largest number of points on thelogarithm of the corrected urea concentration curve. When a portion ofsufficient length has been located, the slope of the curve is determinedfor calculating K/V.

Then, a number of measurement values of the urea concentration, c_(d),is selected which are within a certain deviation from the line obtainedby the Hough transform, for example within 1% from the line. For thesepoints, the instantaneous mass of urea is calculated by using equation(9). Finally, these instantaneous mass values are referenced to timezero, as defined above, by using equation (10) for obtaining severalcalculated values of m₀. The median value of these calculated initialmass values are regarded as the best estimate of the initial mass, m₀,of the body.

Our research has shown that the estimate of the initial urea mass isvery accurate. Thus, the estimate of the efficiency and dose of thetreatment based on this invention are also very accurate.

When the initial urea mass, m₀, has been obtained, it can be used inmany different ways to estimate the efficiency of the treatment.

The dose of the treatment can be calculated by using equation (11) toobtain K/V at each moment of time. Then, K/V is integrated over the timeto obtain Kt/V. When the desired dose has been obtained, the dialysistreatment is terminated.

If the distribution volume, V₀, of urea in the body is estimated, theinitial urea blood concentration, c_(b pre), in the body can be obtainedwithout the need for taking any blood sample by dividing the estimatedmass, m₀, by the distribution volume, V₀. Since the total removed urea,U, is calculated continuously, the urea mass after the dialysistreatment is known and the post urea blood concentration, c_(b post),can be estimated since ultrafiltration is also known. The post ureaconcentration is the equilibrated urea concentration, since the methodaccording to the present invention calculates on total urea mass in thebody.

Thus, URR or SRI can be calculated according to equations (2) or (3).Moreover, equation (1) can be used for estimating the dialysis dose,Kt/V.

The value obtained by determination of the initial mass, m₀, can be usedfor calculating the urea distribution volume, V, of the patient, forexample after completion of the dialysis session. First, the initialurea concentration in blood, c_(b pre), is measured before the dialysisto obtain a value of the mean urea concentration before dialysis, forexample by a blood sample or equilibrated dialysate measurement. Thisurea concentration is equal to the “mean” urea concentration accordingto the present invention, since urea is initially equally distributed inthe body of a patient. Then, the distribution volume, V_(pre), (V₀) canbe calculated by dividing the initial urea mass, m₀, as calculatedaccording to the present invention with measured blood concentration,c_(b pre). Finally, the ultrafiltration volume removed during thetreatment is subtracted to obtain, V_(post), i.e. the distributionvolume of urea after the dialysis treatment. This post distributionvolume V_(post) should be fairly constant for a normal patient in asteady state and can be used as an additional clinical parameter.

There are many alternative methods of using the principles of thisinvention. For example, it is possible to use the alternative methodwhere K is assumed constant as discussed in relation to equations (16)to (19).

Instead of using the urea concentration values which are within 1% fromthe Hough transform line, the line itself can be used for thecalculations. Moreover, the total removed urea U curve can beapproximated with one or more exponential curves using the Houghtransform.

Other types of curve adaptation algorithms can be used. Thus, it ispossible to use the least squares method. In that case, it is necessaryto remove the data portions where the dialysis machine has made someself-calibration, etc. This can be done in an iterative manner, where afirst approximation is made and all data portions outside a certainlimit, such as 10%, are removed and the process is repeated.

In certain types of dialysis machines, the dialysis treatment isinterrupted regularly for self-calibration of the machine. In that mode,valve 16 is opened while valves 14 and 15 are closed, see FIG. 1. Thus,the dialysis of the blood ceases after a short while when the dialysissolution inside the dialyzer has obtained equilibrium with the blood. Inthe urea concentration curves such self-calibration periods are visibleby regular dips in the curve, see FIG. 5, where such self-calibration iscarried out with 30 minute intervals. After each such self-calibration,the dialysis starts again at a slightly higher level.

In order to account for such intermittent stops in the dialysis, thetime scale should be adjusted to remove a portion of the stop period,since there is obviously no dialysis at least during a portion of thestop period. We have found that the best approximation to reality isobtained if the stop period is replaced by a period of 30 seconds. Thisis substantially independent of the actual length of the stop period,which can be anything from 35 seconds to several minutes.

As explained above, it is possible with the present invention to obtaina value of the initial mass of urea in the body of a patient. Thepresent invention can also be utilised in other areas, where it is ofinterest to know the mass of a substance or composition, such as in abeer brewery.

Substances other than urea can be monitored, such as creatinine, sodium,potassium, calcium, magnesium, bicarbonate, glucose, β₂-microglobuline,etc. It is also possible to monitor the conductivity of the plasma wateror blood, or the osmolarity thereof. It is also possible to use theprinciples of the present invention in connection with gases, such asoxygen gas, nitrogen gas or carbon dioxide gas.

If the present invention is to be used for compositions in the bodyhaving some active mechanism interfering in the body, such as for sodiumand potassium ions, such interaction should be taken into account.

For sodium and potassium and some other solutes, it is customary toinclude some concentration of these ions in the fresh dialysis solutionand therefor it is necessary to calculate the difference between initialconcentration and final concentration in the effluent dialysate from thedialyzer. One approach is to replace the concentration value, c_(d), bythe concentration difference, c_(dout), minus c_(din) and the meanconcentration, c_(m), by the difference between the mean concentrationand the initial dialysis fluid concentration, i.e. c_(m) minus c_(din).Consequently, equation (4) at page 9 will essentially be replaced by:

K=Q _(d)·(c _(dout) −c _(doin))/(c _(m) −c _(din))  (22)

If the treatment has followed a standard treatment with no apparentcomplications, the dialysis dose can be calculated by using the initialand final dialysate urea concentrations, c_(dpre) and C_(dpost), andusing the equation:

URR=1−c _(d post) /c _(d pre)  (23)

If the URR calculated using the method according to the presentinvention differs substantially from the URR obtained with equation(23), it is an indication of problems during the dialysis, such asclotting of the dialyzer, which otherwise could have passed undetected.

For determining the urea mass by equations (15) or (19) it is assumedthat the concentration follows an exponential curve over at least aportion of the curve. Since the removed urea mass U is the integral ofthe concentration, c_(d), multiplied by the dialysate flow, Q_(d),(which is constant), it follows that U is also an exponential curve overat least a portion thereof. Consequently, it is possible to use Uinstead of c_(d) for calculating the momentary relative efficiency.

Alternatively, U can be used for verifying that the calculations usingthe concentration c_(d) are correct. Thus, it can be assumed that Uapproaches an asymptote which is:

Asy=m ₀ +G·t−G/(K/V)  (24)

Since all these constants are obtained from the equations given above,it is easy to calculate U minus Asy to see if this curve is anexponential curve with the same exponent as the concentration curve. Ifthis is not the case, there is probably some error.

According to the present invention, the initial mass of urea isdetermined and several clinical parameters are calculated therefrom.However, the blood concentration of urea cannot be obtained, but needsto be measured by taking a blood sample and analysing it later, or byequilibrated ultrafiltration before the dialysis treatment is started.However, it is possible to determine the effective clearance of thedialyzer with a method where a disturbance is introduced into thedialyzer and the resultant effect on the effluent dialysate is analysed.

Such a method is shown in FIG. 9 which is a schematic view similar toFIG. 2. In the dialysis circuit is added a pump 24 connected to theinlet of the dialyzer between the valve 14 and the dialyzer 1. To theother side of the pump 24 is connected a bag 25 comprising a material tobe added to the dialysis circuit by means of pump 24.

Moreover, FIG. 9 shows a pump 26 connected to the blood circuit at theinlet of the dialyzer 1 for introducing a material comprised in a bag 27connected to the other side of the pump 26.

Any of these devices can be used for introducing a disturbance to theinlet of the dialyzer. It is also possible to produce a disturbance byoperating the concentrate pumps 8 and/or 9.

The disturbance is a change of a parameter of the dialysis fluid or theblood. The disturbance can be a change of the conductivity or a changeof the urea concentration. It is noted that the urea monitor can measureboth urea concentration and conductivity in the effluent dialysate. Ifanother measurement instrument is used, any other substance can be usedas a disturbance, as soon as it is compatible with the body, such assodium, bicarbonate, etc.

The influence by the dialyzer on the disturbance is measured downstreamof the dialyzer, for example by the urea sensor. A portion of thedisturbing material will pass the membrane from the dialysate to theblood or vice versa. The amount passing the membrane is dependent on thedialysance of the membrane.

If the disturbance is a step change in the conductivity, produced bypumps, 8 and 9, the dialysance of the dialyzer can be determinedaccording to equation (see European Patent No. 547,025, the contents ofwhich is incorporated herein by reference thereto).

D _(e) =Q _(d)[1−(c _(dout2) −c _(dout1))/(c _(din2) −c _(din1))]  (25)

where

D_(e)=effective dialysance of the dialyzer

Q_(d)=effluent dialysate flow

c_(dout1) and c_(dout2)=concentration in the effluent dialysate

c_(din1) and c_(din2)=concentration in the introduced dialysis fluid

Indexes 1 and 2 indicates before and after the step change. Theintroduced concentration can be measured, or it can be determined by theset values of the concentration pumps.

It is also possible to determine the effective dialysance of thedialyzer by the method disclosed in European Patent No. 658,352 wherethree concentrations are measured and the dialysance is determined asdisclosed in that patent specification, the contents of which areincorporated herein by reference thereto.

An alternative method of determining the effective dialysance isdisclosed in European Patent Application No. 97/15818, the contents ofwhich are incorporated herein by reference thereto. The dialysance isdetermined by the formula:

D _(e) =Q _(d)×(1−S _(out) /S _(in))  (26)

where:

D_(e)=effective dialysance of the dialyzer

Q_(d)=dialysate flow emitted from the dialyzer

S_(out)=integral of Qd×(cd(t)−cd0) during the disturbance in the flowemitted from the dialyzer S_(in)=integral of Qd×(cd(t)−cd0) during thedisturbance in the flow entered into the dialyzer

The disturbance can be a change of conductivity or a change of ureaconcentration or any other substance that can be measured and iscompatible with the body.

After obtaining the effective clearance of the dialyzer with any of theabove-mentioned method, it is observed that the urea monitor measuresthe concentration of urea in the effluent fluid continuously. Thus, theurea concentration at the start of the treatment can be extrapolatedfrom the first 5 to 20 minutes of treatment as shown in FIG. 10. Then,the plasma water concentration of urea in the body at the start of thetreatment can be determined according to the formula:

c _(pw) =Q _(d) ×c _(d) /K _(e)  (27)

where

c_(pw)=plasma water concentration of urea at initiation of dialysis

Q_(d)=effluent dialysate flow rate

c_(d)=concentration of urea as extrapolated to the initiation

K_(e)=effective clearance of the dialyzer for urea

Since the plasma water concentration of urea can be calculated asindicated above and the amount of urea at the start of the treatment isestimated according to the present invention, the distribution volume Vof urea in the body can be calculated. This distribution volume V is animportant clinical parameter, which now can be measured with highaccuracy.

The present invention has been described in connection with removing asubstance from the body, such as urea. The same principle is valid forthe addition of a substance to the body, such as bicarbonate, acetate orlactate, etc.

The present invention has been described in connection with a ureamonitor, which measures the urea concentration in the dialysatecontinuously. It is also possible to use a measurement apparatus whichmeasures the concentration intermittently, for example with one or a fewminutes interval.

In principle, the present invention can also be used for peritonealdialysis, where the effluent dialysate is monitored for a certainsubstance or composition. Specially at tidal automatic peritonealdialysis, where the dialysate in the patient is partially replacedperiodically, the principles of this invention could be applied.

Although the invention herein has been described with reference toparticular embodiments, it is to be understood that these embodimentsare merely illustrative of the principles and applications of thepresent invention. It is therefore to be understood that numerousmodifications may be made to the illustrative embodiments and that otherarrangements may be devised without departing from the spirit and scopeof the present invention as defined by the appended claims.

What is claimed is:
 1. A method for calculating a parameter of the massexchange of a solute in a fluid comprising: passing said solute in apredetermined volume of said fluid on one side of a semi-permeablemembrane in a mass exchange device, passing an exchange fluid on theother side of said semi-permeable membrane, obtaining a soluteconcentration curve by repeatedly measuring the concentration of saidsolute in said exchange fluid, fitting an approximation curve having alogarithm comprising a substantially straight line with at least aportion of said concentration curve, determining a parameter of saidapproximation curve, and calculating the mass of said solute in saidpredetermined volume of said fluid by the formula m=(Q_(d)·c_(d))/Pwherein m comprises said mass of said solute, Q_(d) comprises the flowrate of said exchange fluid, c_(d) comprises the concentration of saidsolute in said exchange fluid, and P comprises said parameter.
 2. Themethod of claim 1 including determining the flow rate of said exchangefluid, integrating the product of said flow rate of said exchange fluidand said concentration of said solute in said exchange fluid over timein order to calculate the accumulated mass of said solute in saidexchange fluid, and calculating a solute reduction index by the formula:SRI=(U−G·t)/(m+U−G·t) wherein SRI comprises said solute reduction index,U comprises said accumulated mass of said solute in said exchange fluid,G comprises the production of said solute over time, and t comprisestime.
 3. The method of claim 1 wherein said mass exchange devicecomprises a dialyzer, said mass exchange fluid comprises a dialysatefluid, and said solute comprises urea.
 4. The method of claim 1 whereinsaid parameter corresponds to a whole body clearance divided by saidpredetermined volume of said fluid.
 5. The method of claim 1 whereinsaid passing of said exchange fluid on said other side of saidsemi-permeable membrane comprises passing a finite initial concentrationof said solute and wherein said measuring of said solute concentrationcomprises repeatedly measuring the difference of said soluteconcentration across said semi-permeable membrane.
 6. The method ofclaim 1 wherein said fitting of said approximating curve comprisesobtaining a compensated concentration by subtracting a predeterminedconcentration term from said concentration of said solute, obtaining thelogarithm of said compensated concentration, and fitting a straight lineto said logarithm of said compensated concentration, whereby saidpredetermined concentration term compensates for the generation of saidsolute.
 7. The method of claim 1 wherein said parameter of saidapproximation curve comprises a slope of said substantially straightline.
 8. The method of claim 1 wherein said fitting of saidapproximation curve excludes a predetermined initiation period.
 9. Themethod of claim 8 wherein said predetermined initiation period comprisesabout 60 minutes.
 10. The method of claim 1 including periodicallyinterrupting said passing of said exchange fluid on said other side ofsaid semi-permeable membrane for a first time period, and adjusting thetime scale by replacing said first time period with a second timeperiod, said second time period being less than said first time period.11. The method of claim 1 wherein said parameter comprises a slope withrespect to time in the following equation: ln (c _(d) −G/Q _(d))=ln (c ₀−G/Q _(d))−Kt/V  (I) wherein c_(d) comprises the concentration of saidsolute in said exchange fluid, G comprises the production of said soluteover time, c₀ comprises the concentration of said solute in saidexchange fluid at time zero, K/V comprises the relative whole bodydialysis efficiency, and t comprises the time from time zero.
 12. Themethod of claim 11 including determining the momentary mass by theequation: m ₁=(Q _(d) ·c _(d1))/(K/V)₁ wherein (K/V)₁ is determined inaccordance with equation (I), and including determining the momentaryrelative efficiency at a predetermined time by the equation: (K/V)₂=(Q_(d) ·c _(d2))/m ₂  wherein (K/V)₂ comprises said momentary relativeefficiency, m₂ comprises m₁−(U₂−U₁)+G (t₂−t₁), c_(d1) comprises theconcentration of said solute in said exchange fluid at time t₁, c_(d2)comprises said concentration of solute in said exchange fluid at timet₂, U₁ comprises the accumulated mass of said solute in said exchangefluid at time t₁, and U₂ comprises the accumulated mass of said solutein said fluid at time t₂.
 13. The method of claim 12 includingintegrating said relative dialysis efficiency over time, whereby anestimate of the total dialysis dosage can be obtained.
 14. The method ofclaim 12 wherein said fitting of said approximation curve comprisescalculating a line passing through the greatest number of points in saidlogarithm of said concentration curve.
 15. The method of claim 14wherein said calculating is compensated.
 16. The method of claim 14including calculating said momentary mass from all values of saidconcentration of said solute in said exchange fluid from saidsubstantially straight line within a predetermined time period,calculating a calculated initial mass from said momentary mass, andestimating the actual initial mass from said calculated initial mass.17. The method of claim 16 wherein said estimating of said actual masscomprises determining the mean or median value of said calculatedinitial mass.
 18. The method of claim 11 including determining themomentary mass of said solute in said exchange fluid by determining theactual concentration of said solute in said exchange fluid by a methodselected from the group consisting of analyzing a blood sample andequilibrating said exchange fluid with blood and determining thedistribution value of said solute.
 19. The method of claim 1 includingestimating the distribution volume of said fluid, and determining theconcentration of said solute in said fluid by dividing said calculatedmass by said distribution volume.
 20. The method of claim 19 whereinsaid estimating of said distribution volume is carried out utilizingWatson's formula.
 21. The method of claim 1 including measuring theconcentration of said solute in said fluid and determining thedistribution volume of said solute in said fluid by dividing thecalculated mass and said concentration of said solute in said fluid. 22.The method of claim 3 including introducing a disturbance into saiddialyzer and measuring the resulting effect in said dialysate, wherebythe concentration of said solute in said fluid is measured, calculatingthe effective clearance of said dialyzer from said measured resultingeffect on said dialysate, calculating the plasma water concentration ofsaid solute utilizing the formula c _(pw) =Q _(d) ×c _(d) /K _(e)wherein c_(pw) comprises the plasma water concentration of urea uponinitiation of said dialysis, Q_(d) comprises the effluent dialysate flowrate from said dialyzer, c_(d) comprises the concentration of ureaextrapolated to initiation of said dialysis, and K_(e) comprises theeffective clearance of said dialyzer for urea; and determining thedistribution volume of said urea in said fluid by means of the formula:V=m ₀ /c _(pw)  wherein m₀ comprises said initial mass.
 23. The methodof claim 1 including determining a deviation of said concentration curvefrom said approximation curve, and emitting an alarm based upon saiddeviation with respect to a predetermined threshold level.
 24. Themethod of claim 3 wherein said parameter comprises the slope ofln(c_(d)−c_(k)) as a function of (V₀/UF)ln(V/V₀) in the equation: ln (c_(d) −c _(k))=ln (c ₀ −c _(k))+[(K−UF)/V ₀]·[(V ₀ /UF) ln (V/V ₀)]  (II)wherein c_(d) comprises the concentration of said dialysate at time t,c₀ comprises the concentration of said dialysate at time zero, c_(k)comprises G/[Q_(d) (1−UF/K)], G comprises the generation of said solute,Q_(d) comprises the flow rate of said dialysate, K comprises the wholebody clearance, V₀ comprises the distribution volume prior to treatment,UF comprises the ultrafiltration per unit time, and [(K−UF)/V₀]comprises said slope.
 25. The method of claim 24 comprising determiningsaid momentary mass according to the equation: m ₁=(Q _(d) ·c_(d1))/(K/V)₁ wherein (K/V)₁=(K/V ₀)/(1−t ₁ ·UF/V ₀) and (K/V₀) isdetermined according to equation (II) and including estimating UF/V₀,wherein said momentary relative efficiency at a given time is determinedaccording to the equation: (K/V)₂=(Q _(d) ·c _(d2))/m ₂ wherein m ₂ =m₁−(U ₂ −U ₁)+G (t ₂ −t ₁) and c_(d1) comprises the concentration of saiddialysate at time t₁, c_(d2) comprises the concentration of saiddialysate at time t₂, U₁ comprises the accumulated mass of said soluteat time t₁, and U₂ comprises accumulated mass of said solute at time t₂.26. Apparatus for calculating a parameter of a mass exchange procedurecomprising: mass exchange means for passing a solute in a predeterminedvolume of a fluid on one side of a semi-permeable membrane and passing amass exchange fluid on the other side of said semi-permeable membrane inorder to exchange said mass of said solute therebetween; measuring meansfor measuring the concentration of said solute in said mass exchangefluid, whereby a solute concentration curve can be provided; firstcalculation means for fitting an approximation curve having a logarithmcomprising a substantially straight line to at least a portion of saidsolute concentration curve; second calculation means for determining aparameter of said approximation curve; and third calculation means forcalculating the mass of said solute in said predetermined volume of saidfluid by means of the formula m=(Q _(d) ·c _(d))/P  wherein m comprisessaid mass of solute in said predetermined volume of said fluid, c_(d)comprises the concentration of said solute in said mass exchange fluid,P comprises said parameter, and Q_(d) comprises the flow rate of saidmass exchange fluid.
 27. The apparatus of claim 26 including flow ratedetermination means for determining said flow rate of said mass exchangefluid, fourth calculation means for calculating the accumulated mass ofsaid solute in said mass exchange fluid from said mass exchange flowrate and said concentration of said solute by integrating the product ofsaid mass exchange flow rate and said solute concentration in said massexchange fluid over time, and fifth calculation means for calculating asolute reduction index according to the formula: SRI=(U−G·t)/(m+U−G·t)wherein SRI comprises said solute reduction index, G comprises theproduction of said solute over time, and t comprises time.
 28. Theapparatus of claim 27 wherein said mass exchange means comprises adialyzer, said exchanging of said solute between the sides of saidsemi-permeable membrane comprises dialysis, said mass exchange fluidcomprises a dialysate fluid, and said solute comprises urea.
 29. Theapparatus of claim 28 including flow rate measuring means for measuringthe flow rate of said dialysate, and wherein said third calculationmeans includes means for calculating the accumulated mass of said ureain said dialysate by integrating the product of said flow rate of saiddialysate and the concentration of said solute in said dialysate fluidover time.
 30. The apparatus of claim 28 wherein said dialysate fluidhas an initial concentration of said urea which is greater than zero,and wherein said measuring means measures the concentration differenceacross said semi-permeable membrane.
 31. The apparatus of claim 28wherein said first calculation means includes means for subtracting afirst compensation term comprising G/Q_(d) from said concentration ofsaid urea in order to obtain a compensated concentration, whereby astraight line can be fitted to the logarithm of said compensatedconcentration so that said compensation term compensates for theproduction of said urea over time.
 32. The apparatus of claim 21 whereinsaid parameter comprises the slope of said substantially straight line.33. The apparatus of claim 21 wherein said first calculation meansincludes means for excluding data obtained during said initiationperiod.
 34. The apparatus of claim 33 wherein said initiation periodcomprises about 60 minutes.
 35. The apparatus of claim 28 wherein saidfirst calculation means includes means for adjusting the time scalewhereby when said flow of said dialysate fluid is interrupted for afirst time period said first time period can be replaced with a secondtime period, said second time period being shorter than said first timeperiod.
 36. The apparatus of claim 28 wherein said parameter comprisesthe slope with respect to time, and wherein said second calculationmeans includes means for calculating said parameter by means of thefollowing equation: ln (c _(d) −G/Q _(d))=ln (c ₀ −G/Q _(d))−Kt/V  (I)wherein c_(d) comprises the concentration of said dialysate at time t, Gcomprises the generation of said urea, Q_(d) comprises the flow of saiddialysate fluid, c₀ comprises the concentration of said dialysate fluidat time zero, K/V comprises the relative dialysis efficiency, and tcomprises the time from time zero.
 37. The apparatus of claim 36 whereinsaid second calculation means includes means for calculating a momentarymass according to the equation: m ₁=(Q _(d) ·c _(d1))/(K/V)₁ wherein m₁comprises said momentary mass, (K/V)₁ is determined according toequation (I), and the momentary relative efficiency at any time isdetermined according to the equation: (K/V)₂=(Q _(d) ·c _(d2))/m ₂ wherein (K/V)₂ comprises said momentary relative efficiency, m ₂ =m₁−(U ₂ −U ₁)+G(t ₂ −t ₁),  c_(d1) comprises the concentration of saiddialysate fluid at time t₁, c_(d2) comprises the concentration of saiddialysate fluid at time t₂, U₁ comprises the accumulated mass of saiddialysate fluid at time t₁, and U₂ comprises the accumulated mass ofdialysate fluid at time t₂.
 38. The apparatus of claim 37 wherein saidsecond calculation means comprises means for integrating said relativedialysis efficiency over time whereby an estimate of the total dialysisdose is provided.
 39. The apparatus of claim 26 wherein said secondcalculation means comprises means for fitting said approximation curveby calculating a line passing through the greatest number of points inthe logarithm of said concentration curve.
 40. The apparatus of claim 39wherein said calculation means includes means for calculating themomentary mass of said solute using the values of said concentration ofsaid solute in said mass exchange fluid within a predetermined limitfrom said substantially straight line which can then be used tocalculate the initial mass of said solute, which can be used to estimatethe actual initial mass of said solute.
 41. The apparatus of claim 39wherein said second calculation means further includes means forestimating said actual initial mass based upon the median or mean valueof said initial mass.
 42. The apparatus of claim 37 including means fordetermining a momentary mass of said solute by analyzing a blood sampleor by equilibration of said dialysate with blood and determining theactual concentration of said solute and measuring the distributionvolume of said solute.
 43. The apparatus of claim 28 including means forestimating the distribution volume of said dialysate and for determiningthe concentration of said urea in said dialysate by dividing saidcalculated mass by said volume.
 44. The apparatus of claim 43 whereinsaid means for estimating said distribution volume utilizes Watson'sformula.
 45. The apparatus of claim 28 including means for measuring theconcentration of said urea in said dialysate and for determining thedistribution volume by dividing said calculated mass by saidconcentration.
 46. The apparatus of claim 28 wherein said measuringmeans comprises means for introducing a disturbance into said dialyzer,means for measuring the resulting effect in said dialysate and forcalculating the effective clearance of said dialyzer from said resultingmeasurements, means for calculating the plasma water concentration ofsaid solute by the formula: c _(pw) =Q _(d) ·c _(d) /K _(e) whereinc_(pw) comprises the plasma water concentration of urea at theinitiation of said dialysis, Q_(d) comprises the flow rate of saiddialysate, c_(d) comprises the concentration of said urea extrapolatedto said initiation of said dialysis procedure, K_(e) comprises theeffective clearance of said dialyzer for urea, and including means fordetermining the distribution volume V of said urea using the formulaV=m₀/c_(pw) where V comprises said distribution volume.
 47. Theapparatus of claim 28 including means for determining a deviation ofsaid concentration curve from said approximation curve and alarm meansfor emitting an alarm upon deviation greater than a predeterminedthreshold level.
 48. The apparatus of claim 28 wherein said parametercomprises a slope and wherein said second calculation means comprisesmeans for calculating said slope in the equation: ln (c _(d) −c _(k))=ln(c ₀ −c _(k))+[(K−UF)/V₀]·[(V ₀ /UF) ln (V/V ₀)]  (II) wherein[(K−UF)/V₀] comprises said slope of a predetermined line,ln(c_(d)−c_(k)) comprises said line, c_(d) comprises the concentrationof said dialysate at time t, c_(k) comprises G/[Q_(d) (1−UF/K)], Gcomprises the generation of said urea, Q_(d) comprises the flow of saiddialysate, c₀ comprises a concentration of said dialysate at time zero,K/V comprises the relative dialysis efficiency, and UF comprises theultrafiltration over time.
 49. The apparatus of claim 48 wherein saidsecond calculation means includes means for calculating a momentary massaccording to the equation: m ₁=(Q _(d) ·c _(d1))/(K/V)₁ wherein(K/V)₁=(K/V ₀)/(1−t ₁ ·UF/V ₀), (K/V₀) is determined according toequation (II) and UF/V₀ is estimated, and the momentary relativeefficiency at any given predetermined time is determined according tothe equation: (K/V)₂=(Q _(d) ·c _(d2))/m ₂  where (K/V)₂ comprises saidmomentary relative efficiency, m ₂ =m ₁−(U ₂ −U ₁)+G (t ₂ −t ₁)  andc_(d1) comprises the concentration of said urea at time t₁, c_(d2)comprises the concentration of said urea at time t₂, U₁ comprises theaccumulated mass of said urea at time t₁, and U₂ comprises theaccumulated mass of said urea at time t₂.